Two gases $A$ and $B$ having same pressure $P$ , volume $V$ and temperature $T$ are mixed. If the mixture has volume and temperature as $V$ and $T$ respectively, then the pressure of the mixture will be

4 P

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3 P

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2 P

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P

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Solution

The correct option is C $2 P$

where, $n =$ no. of moles
$P =$ pressure
$V =$ volume
$T =$ Temperature
Ideal gas equation,
$P V = n R T ∴ n_{A} = \frac{P V}{R T}$ and

$n_{B} = \frac{P V}{R T} \Rightarrow n_{A} + n_{B} = \frac{2 P V}{R T}$
For mixture,
$P^{'} V = (n_{A} + n_{B}) R T \Rightarrow P^{'} = \frac{2 P V}{R T} \times \frac{R T}{V} = 2 P$

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